Unconventional criticality, scaling breakdown, and diverse universality classes in the Wilson-Cowan model of neural dynamics

TL;DR

This paper explores various phase transitions in the stochastic Wilson-Cowan neural model, revealing new types of critical behavior and scaling breakdowns relevant to neural avalanches and non-equilibrium phase transitions.

Contribution

It identifies eight types of phase transitions, including novel ones, and analyzes their critical properties, extending the understanding of neural network dynamics and universality classes.

Findings

Eight types of phase transitions identified

Discovery of novel transition behaviors including scaling breakdown

Relevance to neural avalanche phenomena

Abstract

The Wilson-Cowan model constitutes a paradigmatic approach to understanding the collective dynamics of networks of excitatory and inhibitory units. It has been profusely used in the literature to analyze the possible phases of neural networks at a mean-field level, e.g., assuming large fully-connected networks. Moreover, its stochastic counterpart allows one to study fluctuation-induced phenomena, such as avalanches. Here, we revisit the stochastic Wilson-Cowan model paying special attention to the possible phase transitions between quiescent and active phases. We unveil eight possible types of phase transitions, including continuous ones with scaling behavior belonging to known universality classes -- such as directed percolation and tricritical directed percolation -- as well as novel ones. In particular, we show that under some special circumstances, at a so-called Hopf tricritical directed percolation transition, rather unconventional behavior including an anomalous breakdown of scaling emerges. These results broaden our knowledge of the possible types of critical behavior in networks of excitatory and inhibitory units and are of relevance to understanding avalanche dynamics in actual neuronal recordings. From a more general perspective, these results help extend the theory of non-equilibrium phase transitions into quiescent or absorbing states.